j-multiplicity

In algebra, a j-multiplicity is a generalization of a Hilbert–Samuel multiplicity. For m-primary ideals, the two notions coincide.

Definition

Let be a local Noetherian ring of Krull dimension . Then the j-multiplicity of an ideal I is

where is the normalized coefficient of the degree d  1 term in the Hilbert polynomial ; means the space of sections supported at .

References

  • Daniel Katz, Javid Validashti, Multiplicities and Rees valuations
  • Katz, Daniel; Validashti, Javid (2010). "Multiplicities and Rees valuations". Collectanea Mathematica. 61: 1–24. doi:10.1007/BF03191222. Zbl 1216.13016.
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